Question

Imagine a new pasture with grass growing on it. Every day after the seeds have germinated, the number of blades of grass in the pasture triples. After 18 days, the entire pasture is completely covered in grass. How many days did it take for the pasture to be one-third covered in grass?

Answer 1

It took 17 days for the pasture to be one-third covered in grass

Explanation:

* Lets explain how to solve the problem

- The number of blades of grass is triple every day

- Consider that there are x blades in the first day

∵ The number of blades of grass is triple every day

∴ The next day the number of blades of grass will be 3x

∴ The formula to find the number of blades of grass after d days is

`x(3)^(d)`

- After 18 days, the entire pasture is completely covered in grass

∵ d = 18

∴ The number of blades of grass =
`x(3)^(18)`

- We need to know the the number of days that took for the pasture

to be one-third covered in grass

∵ The number of blades of grass for 1/3 covered =
`((1)/(3))x(3)^(18)`

∴
`((1)/(3))x(3)^(18)=x(3)^(d)`

- Remember
`(1)/(3)=3^(-1)`

∴
`3^(-1)x(3)^(18)=x(3)^(d)`

- Remember we add the power of the same bases when we

multiply them

∴
`x(3)^(-1+18)=x(3)^(d)` ⇒ divide both sides by x

∴
`(3)^(17)=(3)^(d)`

- Remember if the two bases equal in the equation, then their

powers are equal

∴ d = 17

* It took 17 days for the pasture to be one-third covered in grass